In the last decade, I've had ~5 LOA recipients who were fully qualified but didn't get a nom. They all received turndowns.
Why, you ask, would an LOA recipient NOT get a nom? The main reason, I suspect from my small sample size, is that they don't come across well in the interview and/or the MOC committee believed there were 10 more qualified candidates. Remember that USNA Admissions doesn't meet candidates (other than thru a BGO) before offering a nom and sometimes gives out an LOA before the BGO interview. And, even an "awkward" BGO interview is unlikely to derail an otherwise great candidate. Thus, there are some folks who are terrific "on paper" but who just don't present well for any number of reasons (too shy, can't answer basic questions, come across as a know-it-all).
In a few cases (thankfully, very few) MOCs may try to "game the system" by refusing to nominate LOA recipients on the (incorrect, at least for USNA) theory that USNA will "find" the LOA candidate a nom and thus the MOC will get an extra appointment -- one from his/her slate and the other (LOA recipient) who will get a nom from another source. Sadly, that doesn't always work out well for the LOA candidate and, as noted, is very rare.